The grades on a math midterm at Springer are normally distributed with $\mu = 76$ and $\sigma = 2.0$. Ishaan earned a $79$ on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ishaan's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{79 - {76}}{{2.0}}} $ ${ z \approx 1.50}$ The z-score is $1.50$. In other words, Ishaan's score was $1.50$ standard deviations above the mean.